Question

When a ball of weight w rests on a spring of constant k, it produces a static deflection of 3 cm. If the ball is now dropped from a height of h = 30 cm as shown in the figure, the spring will get compressed by

• A. 2.45 cm
• B. 14.07 cm
• C. 16.75 cm
• D. 33 cm

Answer 1

The correct option is C 16.75 cm

$W(h+\delta )=\frac{1}{2}k{\delta }^2$

$W=0.03K$

$0.03K(h+\delta )=\frac{1}{2}K{\delta }^2$

$\frac{1}{0.06}{\delta }^2-0.3-\delta =0\Rightarrow \delta =0.1675m$

$\Rightarrow \delta =16.75cm$